FLC BELIEVED THE ASSIGNED STAR INCLUDED STEPDOWN ALTS. APCH CTL HAD RESTR THE DSCNT FOR DEPS.

Narrative

ALT: 4000 FT. ATC FACILITY: KIN APCH. LOCATION: 17 DME FROM MLY VOR ON ONE ARR. I AM THE CAPT RPTING AND THE PNF. THE EVENT TOOK PLACE AT XA00Z; FREQ 120.6. INITIAL CLRNC BY CTR WAS; ELSER 1 ARR; INTXN/STAR/HDOF TO APCH. AS WE APCHED RADOK INTXN; RECEIVED CLRNC WE UNDERSTOOD TO BE; CLRED ELSER 1 ARR; VOR DME RWY 12 APCH; DSND TO 7000 FT. WE THEN INTERCEPTED THE 17 MI DME ARC AND EXECUTED THE STAR; INCLUDING STEPDOWN ALTS TO 5000 FT AND 4000 FT PER THE STAR. APCH CALLED AND ASKED OUR DME FROM MLY VOR. WE REPLIED 17 DME AT 4000 FT ON THE ARC. APCH CAME RIGHT BACK WITH; YOU SHOULD BE AT 7000 FT. WE WERE JUST ABOUT TO INTERCEPT THE INBOUND COURSE FOR RWY 12 VOR DME APCH. WE UNDERSTOOD WE WERE CLRED FOR THE ARR AND VOR DME APCH TO RWY 12. DO YOU WANT US BACK AT 7000? APCH THEN CAME BACK WITH; CLRED FOR APCH TO RWY 12; EXPECT CIRCLE TO LAND RWY 30; RPT L DOWNWIND TO RWY 30. I GUESS THE MISUNDERSTANDING WAS WHETHER OR NOT WE WERE ACTUALLY CLRED FOR THE APCH. WE THOUGHT WE WERE. THE CTLR SEEMED SURPRISED AT BOTH OUR POS AND OUR ALT. HE HAD JUST CLRED ACR Y FOR TKOF FROM RWY 30 AT THE SAME TIME WE WERE TURNING INBOUND FOR RWY 12. I HAD BEEN INTO KIN SEVERAL TIMES IN THE LAST MONTH AND HAD RECEIVED THE SAME CLRNC AND DIDN'T EXPECT OR NOTICE ANYTHING DIFFERENT THIS TIME INTO KIN UNTIL THE CTLR QUESTIONED OUR ALT.